強健模糊動態輸出回饋控制-Circle 與 Popov 定理

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林玉婷(Yu-Ting Lin) 查詢紙本館藏

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論文名稱

強健模糊動態輸出回饋控制-Circle 與 Popov 定理

相關論文

★ 強健性扇形區域穩定範圍之比較	★ 模糊系統混模強健控制
★ T-S模糊模型之建構、強健穩定分析與H2/H∞控制	★ 廣義H2模糊控制-連續系統線性分式轉換法
★ 廣義模糊控制-離散系統線性分式轉換法	★ H∞模糊控制－連續系統線性分式轉換法
★ H∞模糊控制—離散系統線性分式轉換法	★ 強健模糊觀測狀態回饋控制-Circle與Popov定理
★ H_infinity 取樣模糊系統的觀測型控制	★ H∞取樣模糊系統控制與觀測定理
★ H-ihfinity取樣模糊系統動態輸出回饋控制	★ H∞模糊系統控制-多凸面法
★ H∞模糊系統控制-寬鬆變數法	★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測
★ 寬鬆耗散性模糊控制-波雅定理	★ 耗散性估測器-波雅定理

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摘要(中)

本篇論文主要分為兩部分：
1.經由事先給定非線性系統的動態方程式，將此系統精確的轉換成 Takagi-Sugeno (T-S) 模糊模型。設計動態輸出回授控制器來穩定連續及離散 T-S 模糊模型並滿足圓定理（Circle theorem）的穩定條件。
2.同樣將經由事先給定非線性系統的動態方程式，將此系統精確的轉換成Takagi-Sugeno (T-S) 模糊模型。設計動態輸出回授控制器來穩定連續及離散 T-S 模糊模型並滿足Popov 定理（Popov theorem）的穩定條件。
本篇論文不同於以往的部分在於我們是從時域切入，並且在絕對穩定（Absolute stability）架構中將原為線性系統中的非線性項，改成模糊系統中的非線性項。改變系統架構後，先將非線性系統轉換成T-S 模糊模型，以提供一套系統化的研究方法研究非線性系統的穩定性分析問題。當使用這套方法時，由於控制器是根據 T-S 模糊模型所設計而非直接針對非線性系統做設計，因此若非線性系統與 T-S 模糊模型間誤差為0，則此控制法則可用於非線性系統。
為確保系統與模型之間的誤差為零，本篇論文沿用一個方法將誤差以有界非線性項 (sector-bounded nonlinearities) 來表示，而後，非線性系統即可精確的表達成具有非線性項的 T-S 模糊模型。其中非線性項的限制分別須要滿足Circle或 Popov Criteria，若非線性項分別轉換成不確定參數項後，則可視為強健模糊控制。圓定理與Popov 定理最大不同在於他們的Lyapunov函數不同，前者使採用一般的二次Lyapunov 函數，後者則是使用Lure-type Lyapunov函數來證明穩定度的問題。
針對 T-S 模糊模型，本篇論文根據平行分散式補償器 (PDC) 的概念設計控制器。控制系統中，當系統狀態無法完全獲知時，則必須採用估測器獲得所需的資訊或直接以輸出回授做控制，本篇所討論的即是研究動態輸出回授控制器的設計與分析。
在動態輸出回授控制或觀測器方面，最大的問題在於所推導出的穩定條件並非線性矩陣不等式 (LMI) 而是以雙線性矩陣不等式 (BMI)的形式呈現，而 BMI 無法如同 LMI 一般可輕易經由現有工具程式求解。因此，本篇將此部份的重點放在如何求解 BMI 的問題上，透過蕭氏轉換(Schur complement)及全等轉換(congruence transform)的方法可將控制問題中的 BMI 條件轉換為 LMI 形式求解或者經由求解某些 LMI 的子矩陣來達到求解BMI。最後分別以倒單擺及倒車入庫系統的例子來進行電腦模擬。

摘要(英)

關鍵字(中)

★ 雙線性矩陣不等式
★ 線性矩陣不等式
★ Popov定理
★ 圓定理
★ 強健控制
★ 平行分佈補償器
★ T-S模糊模型

關鍵字(英)

★ Popov theorem
★ Lure-type Lyapunov function
★ Linear matrix inequality (LMI)
★ Circle theorem
★ Parallel distributed compensator (PDC)
★ Bilinear matrix inequality (BMI)
★ Robust control
★ Takagi-Sugeno (T-S) fuzzy model

論文目次

第一章簡介 1
{1.1}文獻回顧 1
{1.2}研究動機 2
{1.3}論文結構 3
{1.4}符號標記 4
{1.5}預備定理 4
第一部份：圓定理(Circle Theorem) 6
第二章系統架構與圓定理 6
{2.1}數學模型 6
{2.2}穩定條件 8
第三章動態輸出回饋控制器設計 12
{3.1}數學模型 12
{3.2}廣義動態輸出回饋控制器 13
{3.3}動態輸出回饋控制器 15
{3.3.1}連續系統 15
{3.3.2}離散系統 18
第四章電腦模擬 28
{4.1}倒單擺例子 28
{4.1.1}數學架構 28
{4.1.2}求解 30
{4.2}倒車例子 37
{4.2.1}數學架構 37
{4.2.2}求解 39
第二部份：Popov定理 47
第五章系統架構與Popov定理 47
{5.1}數學模型 47
{5.2}穩定條件 49
第六章動態輸出回饋控制器設計 55
{6.1}數學模型 55
{6.2}廣義動態輸出回饋控制器 56
{6.3}動態輸出回饋控制器 58
{6.3.1}連續系統 58
{6.3.2}離散系統 62
第七章電腦模擬 70
{7.1}倒單擺例子 70
{7.1.1}數學架構 70
{7.1.2}求解 71
{7.2}倒車例子 78
{7.2.1}數學架構 78
{7.2.2}求解 79
第八章總結與未來方向 87
{8.1}總結 87
{8.2}未來研究方向 88
參考文獻 89

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指導教授

羅吉昌(J.C. Lo)

審核日期

2004-6-23

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